CSE 2353 – August 28 th 2002

1. CSE 2353 – August 28th 2002 Logic

2. Propositions • Def: A statement which is True or False • Which are Propositions • This rose is white • Keep off the grass • 7 is even • I am 6 years old • A square has four sides • Did you do your homework

3. Operations • And (conjunction) ^

4. Operations • And (conjunction) ^ • Or (inclusive disjunction) v • Xor (exclusive disjunction) v • Not (negation) ~  • If … then (implication)   • Iff (biconditional)  • Nand | • Nor  • Construct sentences with words

5. Operations • Other Operations

6. Precedence Precedence: () ~ ^ v ->  (TvF)^T = ? Tv(F^T) = ? T v F ^ T = ?

7. Operations

8. Operations

9. Tautologies andContradictions • Tautology: A statement which is True • Contradiction: • p ^ ~p = • p v ~p = • (p^q) v ~(p^q) = • p -> p v q =

10. Practice • Show that (p  q ) implies p

11. Practice • Show that p v q is equivalent to ~(~p ^ ~q) • Show that p^p  p • Show that p q  q p • Show that (p ^ q) ^ r  p ^ (q ^ r) • Show that (p  q)  (~p v q)

12. Summary • Propositions • Operations on Propositions • Truth Tables • Precedence • Tautologies and Contradictions

13. Duality • Swap t,f • Swap ^,v • Example (p ^ q) v ~p • Dual (p v q) ^ ~p • If expressions are equivalent, so are duals

14. Conditionals • Given p  q • Converse q  p • Inverse ~p  ~q • Contrapositive ~q  ~p

15. Arguments • If you insulted Bob then I’ll never speak to you again. You insulted Bob so I’ll never speak to you again. • Premise • Conclusion

16. Arguments • If you are a mathematician then you are clever. You are clever and rich. Therefore If you are rich then you are a mathematician. • Premise • Conclustion